Consider the exponential regime in which \(a_T \sim rT\) , \(r>0\) . [1]} showed that the distributionally robust predictor (REF ) and its associated prescriptor
\(\hat{x}_{\mathrm {KL} ,T }(\mathbb {P}) \in & \operatornamewithlimits{arg\,min}_{x\in \mathcal {X}} \hat{c}_{\mathrm {KL}}(x,\mathbb {P},T),\quad \forall \mathbb {P}\in \mathcal {P}, \; \forall T \in \mathbf {N}\\\in & \operatornamewithlimits{arg\,min}_{x\in \mathcal {X}} \sup _{\mathbb {P}^{\prime } \in \mathcal {P}} \left\lbrace  c(x,\mathbb {P}^{\prime })\ : \  {\mathbb {P}^{\prime }}\le r \right\rbrace ,\quad \forall \mathbb {P}\in \mathcal {P}, \; \forall T \in \mathbf {N}\) 
